Question 718010
x = smallest integer
x + 1 = second integer
x + 2 = third integer {consecutive integers increase by 1}


x(x + 1)(x + 2) = x³ + 21  {product of the three is 21 more than cube of smallest}
(x² + x)(x + 2) = x³ + 21 {used distributive property}
x³ + 3x² + 2x = x³ + 21  {used foil method}
3x² + 2x = 21 {subtracted x³ from each side}
3x² + 2x - 21 = 0 {subtracted 21 from each side}
3x² + 9x - 7x - 21 = 0 {split 2x into 9x and -7x}
3x(x + 3) - 7(x + 3) = 0 {factored 3x out of first two terms and -7 out of last two terms}
(3x - 7)(x + 3) = 0 {factored x + 3 out of the two terms}
3x - 7 = 0 or x + 3 = 0 {set each factor equal to 0}
x = 7/3 or x = -3 {solved each equation for x}
x = -3 {fractions are not integers}
x + 1 = -2 {substituted -3, in for x, into x + 1}
x + 2 = -1 {substituted -1, in for x, into x + 2}


-3, -2, and -1 are the three consecutive integers
<br>For more help from me, visit: <a href = "http://www.algebrahouse.com/" target = "_blank">www.algebrahouse.com</a><br><br>